/sci/ - Science & Math

>>8768728
>>8768742
OP here, it seems to me that STEM is on its way out and no longer useful as seen by the job force. I mean fuck I'm no good at business shit and I hate it but it seems like the only chance I have is to go to school for another 4 years and get a degree in business or accounting. Since science never pays off

kys brainlet there's a stupid question thread over there:
>>8648925

>>8396412
nigger how hard is it for you to use google and look up pde syllabus?

jesus christ this board gets more helpless every year

>vox

>>8380434
>trivial arrangements of group tables
highly non-interesting anon

>>8369360
big surprise, literally 0 indication he's even working on riemann hypothesis

shit thread op

>>8367669
>1) When they say "we can factor p(x) in K[x], do they mean p factors completely into linear factors? Or just that there is some non-trivial
>factorization there? Is it enough to add one root of p to Q, and work in some recursive way?
not every finite extension is a splitting field, and so they certainly don't mean completely into linear factors, just factoring as much as possible in general

i.e. if you want to factor for example the polynomial x^4-10x^2+1, which has roots sqrt(2)+sqrt(3), sqrt(2)-sqrt(3), -sqrt(2)+sqrt(3) and -sqrt(3)-sqrt(2), over the field Q(sqrt(2)) it will factor as (x^2+2 sqrt(2) x-1)(x^2-2 sqrt(2) x-1), but not into linear factors since sqrt(3) is not in your extension

3) I get what L is, I think. We can't say it's a field because p factors. It's a ring.
it is a field if p doesn't factor, but you're right that if you're trying to factor it non-trivially then it's only a ring

>What gets you out of bed each morning to grind that shit out?
nothing

currently number theory grad student

>we as a race thus are given the inadvertent responsibility of being the galaxies caretakers
>we can't have primitive fun anymore and must be a beacon to which other species can aspire too

>the mantle of responsibility belongs to humans